应用集总参数的微机电系统等效电路建模方法研究

Equivalent circuit representation of micromechatronics based on lumped-parameter method

微机电系统(MEMS)的多物理域耦合的特性使得系统建模仿真极为困难。而利用唯象不可逆热力学的相关概念,能够将复杂的MEMS系统分解为多个子系统,并以统一的热力学共轭变量的方式描述各子系统组件模型。由广义Kirchhoffian网络理论,搭建MEMS系统级模型。基于集总参数方法的等效电路方法就是其中一种合适的组件模型表达方式。使用能量变分法建立机、电系统端口变量之间关系的基本方程,获得机械变量与电域变量的转换矩阵,从而建立等效电路模型。模型易于在电系统仿真器中使用,适合于工作平衡点处的小信号仿真。

Modeling and simulation of the micromechatronics system is a really problem due to its multi-physical coupling effects. On the basis of phenomenological irreversible thermodynamics theory, the complex microsystem is decomposed into components and those components can be modeled as multi-terminal network blocks and be described in a generic mathematical description in terms of conjugate thermodynamic state variables. According to the generalized Kirchhoffian network, those multi-terminal blocks can be used for constructing the MEMS system level model. The equivalent circuits based on the lumped-parameter method is one of the quite suitable approaches for representing the multi-terminal component models. The constitutive equation describing the relations between the electronic and the mechanical variables can be deduced by the stored energy differential method, thus the transfer matrix for circuit representation is obtained. The circuit model resulted from the lumped parameter method is easy to use and be easily incorporated into system simulators. It is suitable for analyzing the device response under the small-signal at the bias operation point.